Geodesic
Characterizations of Archimedean $n$-copulas
Kybernetika, Tome 51 (2015) no. 2, pp. 212-230
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We present three characterizations of $n$-dimensional Archimedean copulas: algebraic, differential and diagonal. The first is due to Jouini and Clemen. We formulate it in a more general form, in terms of an $n$-variable operation derived from a binary operation. The second characterization is in terms of first order partial derivatives of the copula. The last characterization uses diagonal generators, which are ``regular'' diagonal sections of copulas, enabling one to recover the copulas by means of an asymptotic representation.
We present three characterizations of $n$-dimensional Archimedean copulas: algebraic, differential and diagonal. The first is due to Jouini and Clemen. We formulate it in a more general form, in terms of an $n$-variable operation derived from a binary operation. The second characterization is in terms of first order partial derivatives of the copula. The last characterization uses diagonal generators, which are ``regular'' diagonal sections of copulas, enabling one to recover the copulas by means of an asymptotic representation.
DOI : 10.14736/kyb-2015-2-0212
Classification : 62H20
Keywords: Archimedean operation; additive generator; diagonal generator; multiplicative generator; (Archimedean) $n$-copula; (Archimedean) $n$-quasicopula 
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Wysocki, Włodzimierz. Characterizations of Archimedean $n$-copulas. Kybernetika, Tome 51 (2015) no. 2, pp. 212-230. doi: 10.14736/kyb-2015-2-0212

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